Integral Problem: Solutions Say Divergent, Help Please!

[Jalo]

Homework Statement

Homework Equations

The Attempt at a Solution

Ive solved it this way:

= [ln |x|]¹_-2 = ln 1 - ln 2 = -ln2

However the solutions say the integral is divergent, therefore it should tend to +∞ or -∞

If someone could tell me what I've done wrong I'd appreciate!
Thanks

 

[D H]

You did two things wrong.

1. Lesser problem: Your integral is incorrect. \int 1/|x|\,dx = \mathop{\mathrm{sgn}} x \, \ln |x|, not \ln |x|.

2. Huge problem: You integrated across a singularity.f(x)=1/|x| is positive everywhere. How could the integral of this function from -2 to 1 possibly be negative? That you obtained a negative result when the integrand is always positive and the integration interval is in the positive direction should have been a big warning sign indicating that you did something wrong.